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RE: Steady state model

From: AVG <avg>
Date: Thu, 6 Aug 2009 09:38:03 +0200

Hello Sherwin,

SS=1 infers a perfect steady state situation, i.e. a particular dosing ev=
ent has been occurring with a particular time interval for infinitely long =
- and nothing else is happening. For the "standard PK model library" in NON=
MEM, i.e. for those linear ODE systems with their analytical (closed form) =
solutions implemented in specific NONMEM Advans, the single dose (SD) solut=
ion is a sum of exponential terms e.g. for a 1st order absorption 1st order=
 elimination 1-cmpt model the solution for conc in the central cmpt is
C(t)= (exp(-K*t)-exp(-Ka*t)) *D*F*Ka/V/(Ka-K). Because all processes in t=
hese models are linear, when you add more doses their individual contributi=
ons to C(t) are additive. So for n doses interspaced by a constant interval=
 tau, with the example model we get
C(t)= (exp(-K*t)+exp(-K*(t+tau))+exp(-K*(t+2tau))...+exp(-K*(t+n*tau)) -e=
xp(-Ka*t)-exp(-Ka*(t+tau))-exp(-Ka*(t+2tau))...-exp(-Ka*(t+n*tau))) *D*F*Ka=
/V/(Ka-K).
This is the sum of two geometric series multplied by a constant, which redu=
ces to
C(t)= (exp(-K*t)*(1-exp(-K*n*tau))/(1-exp(-K*tau)) -exp(-Ka*t)*(1-exp(-Ka=
*n*tau))/(1-exp(-Ka*tau)) *D*F*Ka/V/(Ka-K).
As n tends to infinity, 1-exp(-K*n*tau) and 1-exp(-Ka*n*tau) both tend to 1=
 so for true steady state i.e. infinite n you get the simpler expressions r=
eferred by Samer.

I believe the Gabrielsson & Weiner PKPD book has some of the SS solutions i=
n it.

Best,
Andreas

-----Original Message-----
From: owner-nmusers
 Behalf Of Mouksassi Mohamad-Samer
Sent: 6. august 2009 08:23
To: nmusers
Cc: n.holford
Subject: RE: [NMusers] Steady state model


Hello Sherwin,

All SS routines source code are located at the C:\nmvi\pr folder.

Each Advan closed form model has specific routines (and equations for SS) t=
hat can be used with it.
For linear models the magic factor for steady state computation will be:
exp(-rate.constant.time)/(1-exp(-rate.constant.Tau).
Monolix guide: Monolix31_PKPD_library.pdf has a lot of SS equations for com=
monly used models.

Of course general Advans have their general SS routines too and as Nick men=
tioned there is some root finding going on:

a comment from the SS6.FOR routine reads

C SS IS SOLUTION A OF: 0=DADT(A)+R
C APPROXIMATION: DADT(A)=DADT(0)+DA*A
C 0=DADT(0)+DA*A+R
C A=-DAINV*(DADT(0)+R)
...
Happy Reading !

Bests,

Samer

-----Original Message-----
From: owner-nmusers
Sent: Wed 8/5/2009 15:44
To: nmusers
Subject: Re: [NMusers] Steady state model
 
Sherwin,

I dont understand exactly how NONMEM computes the steady state value but wi=
th ODEs it seems to be done using a numerical root finding procedure i.e. s=
olves for the amt in each of the compartments when all the DEs have a valu=
e of zero.

The amt in each compartment is set to the steady state value. There is no i=
nitial 'parameter' for the compartment. Compartment amounts are variables. =
Parameters are constants. Parameters (e.g. THETA values) are used in the OD=
Es to define the DE values.

Perhaps Alison Boechmann (who wrote the code) could give a more thorough an=
swer?

Nick

Sherwin K Sy wrote:
> Dear NONMEM users,
>
> I'm wondering what equation or ODE is used in NONMEM when the steady
> state is set (i.e. SS = 1). Is it the case that the initial parameter
> for the compartment is set to a different value? If so, how does
> NONMEM set this value?
>
> I would appreciate if anyone can provide me with a reference or point
> me to where I can find this information, including the type of
> equation used for extravascular, iv bolus and iv infusion models.
>
> Thanks,
>
> Sherwin
>
>

--
Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical =
Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Aucklan=
d, New Zealand n.holford
90
mobile: +64 21 46 23 53
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford


Received on Thu Aug 06 2009 - 03:38:03 EDT

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